Methods and systems for substrate surface evaluation

ABSTRACT

A method for determining a surface quality of a substrate sample using a differential interference contrast microscope is described. The microscope includes an eyepiece, an eyepiece focus adjustment, a microscope focus adjustment, a light source, at least one of an aperture or reticule, a camera view, a prism and an eyepiece. The method includes calibrating the focus of the eyepiece with the focus of the camera and determining a peak response ratio for the microscope through adjustment of phase between differential beams of the microscope. The substrate sample is placed under the microscope, illuminated with the light source, and brought into focus with the microscope focus. Phase between differential beams is adjusted, at least one image of the substrate sample is captured and processed to determine a level of surface structure on the substrate sample.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a Continuation Application of application Ser. No.10/376,972 filed Feb. 27, 2003 now U.S. Pat. No. 6,995,847, which claimspriority to Provisional application Ser. No. 60/383,469 filed May 24,2002.

BACKGROUND OF THE INVENTION

This invention relates generally to parts inspection methods and systemsand, more particularly, to evaluation of highly polished substratesurfaces.

Many optical devices, such as ring laser gyroscopes, include highlypolished components, such as substrates utilized in making mirrors.Operation of such devices is greatly dependent upon the quality of themirrors. For example, super-polish quality of a substrate surface, thatis, a lack of scratches and other inconsistencies in the substratesurface, is one factor that determines the amount of light scatteredfrom a polished substrate which has been coated with a reflectivematerial. Currently, subjective inspection techniques are utilized forinspection of polished substrates and have been found inadequate formeasuring super-polished substrate surface quality and maintainingprocesses for producing super-polished surfaces. In one known inspectionprocess, the resolution of the inspection is limited by an amount ofoperator training, operator patience, operator eyesight, as well as anoptical configuration of the inspection system. As such, consistentinspection quality is difficult to achieve.

In another inspection process, the polished substrate surfaces arecoated with a reflective compound and the resultant mirror products areused to evaluate the super-polish quality of the substrate. However,evaluating the super-polish process by using the coated mirror productsdelays feedback to the substrate polishing process and is also subjectto factors external to the polishing process. Further, because thesubstrates are coated with the reflective compound prior to inspection,substrates with flawed surfaces may be coated which increasesmanufacturing costs as more costly pieces (i.e. the coated substrates)may have to be scrapped or reworked. With a better substrate inspectionprocess, flaws in highly polished substrate surfaces could be detected,and possibly corrected, before the reflective compound is applied to aflawed polished surface substrate.

BRIEF SUMMARY OF THE INVENTION

In one aspect, a method for determining a surface quality of a substratesample using a differential interference contrast microscope isprovided. The microscope includes an eyepiece, an eyepiece focusadjustment, a microscope focus adjustment, a light source, at least oneof an aperture or reticule, a camera view, a prism, a reference samplein a fixture, and differential interference optics. The method comprisescalibrating the focus of the eyepiece with the focus of the camera anddetermining a peak response ratio (a ratio of pixel histogram centraltendency location to the exposure time which maximizes the signal tonoise of the surface structure data) for the microscope throughadjustment of phase between differential beams of the microscope. Themethod further comprises placing the substrate sample under themicroscope, illuminating the substrate sample with the light source,focusing on the substrate sample with the microscope focus, andadjusting a phase between differential beams to achieve a peak responseratio. At least one image of the substrate sample is captured andprocessed to determine a level of surface structure on the substratesample.

In another aspect, a substrate inspection system for determining asurface quality of substrate samples is provided. The system comprises adifferential interference contrast microscope that includes an eyepiece,an eyepiece focus adjustment, a microscope focus adjustment, a reticule,a prism, an objective, a camera view, an eyepiece view, and a fixturefor holding a substrate sample. The system further comprises a lightsource, a camera, and a computer for collecting data from the camera andmicroscope. The microscope can be switched between the eyepiece view andthe camera view and the fixture allows adjusting the slope of asubstrate sample to achieve a specified peak response ratio. Thecomputer is configured to capture at least one image of the surfaceslope of the substrate sample, and process images of the surface slopeto determine surface quality and reconstruct an approximate surface ofthe substrate sample.

In still another aspect, a computer program product is used to determinea surface quality of substrate samples. The computer program productincludes code for capturing at least one image of a surface slope of asubstrate sample and code for processing images of the surface slope toreconstruct an approximate surface of the substrate sample.

In yet another aspect, a method for focusing a microscope on a substratesample, the microscope having both a camera field of view and aneyepiece view is provided. The method comprises centering an edge of thesubstrate sample surface in the camera field of view of the microscope,focusing on the edge of the substrate sample surface using the camerafield of view, switching to the eyepiece view, adjusting the eyepiecefocus such that a corner of an aperture of the microscope is in focus,and testing at least one of the eyepiece focus and the camera focus bymoving to an area of the substrate sample that has an identifiablestructure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an inspection system for determiningsubstrate surface quality.

FIG. 2 is an illustration of light beams showing operation of a prismand objective of a microscope with respect to a substrate sample.

FIG. 3 is an illustration of a sample of substrate with an edge with anaperture imposed thereon.

FIG. 4 is a flowchart illustrating a prism calibration method.

FIG. 5 is a flowchart illustrating a substrate surface qualityevaluation method.

DETAILED DESCRIPTION OF THE INVENTION

While the present invention is herein described in the context of aspecific application wherein the invention has been found to beparticularly advantageous, it will be apparent to those skilled in theart that numerous variations or modifications may be made to theexemplary embodiments without departing from the spirit and scope of thepresent invention. It will further be apparent that the advantages ofthe present invention are applicable to other applications andenvironments. Consequently, the exemplary embodiments described hereinare set forth for illustrative purposes only and are not intended tolimit practice of the invention in any aspect. The system and method arenot limited to the specific embodiments described herein. Components ofeach system and method can be practiced independently and separatelyfrom one another. Each system and method also can be used in combinationwith other components and methods.

The methods and systems described herein allow a user to characterizesurfaces of highly polished mirror substrates with high resolution,before they are coated with a reflective compound, and therefore createan opportunity for super polishing process optimization.

FIG. 1 is a block diagram of an inspection system 10 for substrates thatquantitatively measures surface quality of the substrates after apolishing process. The substrates, if found to be acceptable through theinspection process, will eventually be coated with a reflectivecompound. System 10 includes a differential interference contrastmicroscope 12 configured to measure slopes on a surface of a substratesample 24. Slopes detected on substrate sample 24 are used tocharacterize polish quality on the surface of substrate sample 24.Microscope 12 utilizes a light source 14 and a collimator 16 to provideillumination of sample 24 for a low noise and high resolution chargecoupled device (CCD) camera 18, which includes a light detectorsubdivided into a plurality of light-sensing pixels (not shown).Alternatively, an image of substrate sample 24 can be projected to aneyepiece 19, which has a focusing mechanism (not shown). In an exemplaryembodiment, light source 14 is a laser light source, and collimatedlight from light source 14 passes through a reticule 20. Reticule 20 islocated, in one embodiment, such that an optical path of light source 14through microscope 12, through reticule 20 and onto an object, is thesame length as an optical path from a user's eye to an object beingmagnified and from CCD camera 18 to the object being magnified. As it isdesired to view the substrate samples with high bit depth resolution,CCD camera 18, in one embodiment, has 14 bits per pixel bit depthresolution. In one embodiment, CCD camera 18 is aligned so that adifferential shear axis of microscope 12 is along a camera image axis.

Microscope 12 utilizes a Nomarski prism 22 to split linearly polarizedincident light from light source 14 via collimator 16 and polarizer 17into two light beams of orthogonal polarization, which are passedthrough an objective 26, or magnifying portion, of microscope 12. Lightfrom light source 14 reflects off a beamsplitter 23 before enteringNomarski prism 22. When the two light beams illuminate a substratesample 24 held in place utilizing a fixture 28, centers of the lightbeams are separated from each other by a small distance along a sheardirection of prism 22. The separation of the beams at substrate sample24 causes a phase difference between the two light beams wherever asurface of substrate sample 24 is not perpendicular to the optical axisof the prism 22. Upon reflection from a surface of substrate sample 24and retransmission through prism 22, the two orthogonal polarizationsare recombined into a single beam. Differences in phase that are presentin a cross section of the two reflected beams result in polarizationvariation once the beams are recombined. By passing the combined beamthrough an analyzer 29, the polarization variation between the two beamsis converted into an intensity variation. Intensity variation representsvariations in slopes along the surface of substrate sample 24, which isone characterization method for determining polish quality for thesurface of substrate sample 24.

Referring to light source 14, the narrower the bandwidth of the incidentlight, the greater the intensity modulation, which is typical of adifferential interference process. Better collimation also increasesintensity modulation. Using white light for illumination limits theintensity modulation, and therefore resolution of microscope 12 becausewhite light is attenuated significantly during collimation. In analternative embodiment of system 10, light source 14 is a white lightsource and a bandpass filter. In contrast to unfiltered white light, a10 nm wide bandpass filter within collimator 16 can be utilized toimprove the intensity modulation. In use, a 70 nm wide bandpass filterwithin collimator 16 provides an acceptable level of light to CCD camera18 as well as to the operator, while also providing an acceptableintensity modulation and signal to noise ratio.

As described above, one embodiment of system 10 utilizes a laserillumination source for light source 14. The laser illumination sourcehas an ability to increase the signal to noise ratio by orders ofmagnitude, since laser light has a narrow bandwidth and is collimated.When a laser illumination source is used, a rotating diffuser (notshown; in addition to collimator 16) in the optical path is utilized tominimize speckle interference patterns.

A computer 30, which includes a processor (not shown), is programmedwith calibration procedures and analysis techniques to allow a user toachieve a high level of resolution when analyzing surfaces of substrate24 for pits, scratches, and the like. While referred to as a computer,computer 30 is understood to include any and all processor or controllerbased machines which can implement the calibration procedures andanalysis techniques. The procedures and techniques, some of which arerun utilizing computer 30 include, but are not limited to, field of viewcompensation, focus calibration, prism calibration, microscopeoperation, and image processing, which are described below. By employingfield of view compensation, calibration procedures and analysistechniques, system 10 is able to provide a quantitative measurement ofpolish quality on the surface of substrate 24. In addition, theresolution of the optical system provides feedback so that polishingprocesses for substrates can be improved. Further, system 10 evaluatesthe substrates before reflective material is applied to provideimmediate feedback and to prevent reworking of substrates after thereflective material is applied.

FIG. 2 is a detailed illustration of operation of Nomarski prism 22 andobjective 26 with respect to substrate sample 24. Two light beams 42 and44 are separated from one another along a shear direction of prism 22.The separation of beams 42 and 44 at substrate sample 24 causes a phasedifference between the light beams wherever a surface of substratesample 24 is not perpendicular to an optical axis 46 of prism 22. Uponreflection from a surface of substrate sample 24 and retransmissionthrough prism 22, the two orthogonal polarizations are recombined into asingle beam. Differences in phase that had been present in a crosssection of the two reflected beams result in polarization variation oncethe beams are recombined. FIG. 2 is an illustration from the articleHartman et. al., Quantitative surface topography determination byNomarski reflection microscopy. 2: Microscope modification, calibration,and planar sample experiments, Applied Optics, 1 Sep. 1980, Vol. 19, No17.

Field of View Compensation

With regard to field of view compensation, incident light intensity fromlight source 14 varies across the field of view of microscope 12. Fieldof view compensation is accomplished utilizing the methods describedbelow using a differential interference contrast system. To compensatefor the variation, in one embodiment images from several differentlocations on a polished substrate sample of superb quality andcleanliness are collected. Such a sample is sometimes referred to hereinas a reference sample. When pixel intensity values for each of theimages of the reference sample are averaged, an intensity variationcaused by surface imperfections on the reference sample averages toapproximately zero. Therefore, any remaining variation in the resultingaveraged image is considered to be a measure of an intensity variationof the incident light. The resulting image (REF) is utilized tonormalize images of other substrate samples with respect to incidentlight intensity variation. The reference image therefore providescompensation for incident light intensity variations across the field ofview and serves as a partial compensation process for utilization ofmicroscope 12 in substrate surface quality measurement. As used herein,compensation refers to measuring a value of at least one parameter andmaking adjustments based on that parameter to the quantitativemeasurement of substrate quality, if and when such adjustments arenecessary.

Focus Calibration

Focusing on a surface of substrate sample 24 is sometimes difficultsince many magnified images of substrates, particularly super-polishedglass, do not show an obvious structure. In one embodiment, therefore,an aperture 54 (shown in FIG. 3) is located in the incident light pathof microscope 12 at the same distance as the output image distance andthus provides a mechanism for focusing. When edges of aperture 54 are infocus at eyepiece 19 after the incident beams are reflected off sample24, sample 24 is also in focus at eyepiece 19. Typically, focus can beachieved more quickly through eyepiece 19 rather than with the cameraview due to long integration times for most images. Aperture 54 is sizedto be visible only through the larger field of view of eyepiece 19 inorder to maximize the available field of view of camera 18. The abovemethod is referred to as an aperture focus method.

Occasionally, the camera optical path and the eyepiece optical path arenot the same. In this case, a difference between eyepiece aperture focusand camera focus must be compensated, that is, the difference betweeneyepiece aperture focus and camera focus must be determined and, ifnecessary, used to determine the best focusing for the camera field ofview. In one embodiment and as shown in FIG. 3, a substrate sample 50 oranother part with a thickness similar to that of substrate sample 50 isinserted into microscope 12 such that edge 52 is centered in a field ofview of camera 18 (shown in FIG. 1). An eyepiece focus of microscope 12is adjusted until at least one corner 56 of aperture 52 appears focused,then microscope 12 (shown in FIG. 1) is switched to a camera view. Afine focus knob of microscope 12 (shown in FIG. 1) is adjusted so thatedge 52 is focused in the field of view of camera 18. The fine focussetting of microscope 12 is then recorded. In one embodiment, aperture54 is moved along edge 52 of substrate 50 where the focusing process isrepeated a number of times and averaged. The averaged results arerecorded as an eye/camera focus offset. The above described method issometimes referred to as an eye/camera focus offset method.

In another embodiment, one of a crosshairs, an aperture, or a screen isplaced in the incident path at the image distance. When the item (i.e.the crosshairs) is in focus in the output image, substrate sample 24under microscope 12 will also be in focus. Known image processingtechniques based on edge detection are used to automatically determinethe focus status.

Using curve fitting routines or low pass filtering routines withincomputer 30, any curvatures along the surface of substrate sample 24 maybe estimated and removed from the image of the surface of substratesample 24. After the curvature is removed from the image, the remainingintensity variation typically represents undesirable surface structure.

Spherical surfaces under microscope 12 typically follow a well definedmathematical function. If the input intensity variations have beenappropriately compensated across the field of view using the techniquedescribed above, the curvature of a spherical surface may be estimatedby fitting the resulting image with the following function:

(−Gx/[(d²/4) − (x + r sin (θ − ϕ))² − (y + r cos (θ − ϕ))²]^(0.5)) + β + G∇_(x)R(x, y).

-   -   where:    -   d is a diameter of curvature of the spherical surface;    -   r is a distance from a center of the substrate sample;    -   θ is an angle between r and a forward direction of the substrate        sample relative to an operator's perspective;    -   G is a Nomarski crystal constant obtained from calibration;    -   β is a Nomarski crystal background phase obtained from        calibration;    -   (x, y) are spatial coordinates for the substrate sample relative        to a shear direction of the substrate sample;    -   (x′, y′) are spatial coordinates for the substrate sample        relative to an operator's perspective;    -   φ is an angle between the shear direction and x′; and    -   ∇_(x)R(x,y) contains a plurality of roughness slopes for the        substrate sample.

Having an estimate of the curvature provides a method to inspect forflatness or a desired radius of curvature for substrate sample 24. Inaddition, images of substrate sample 24 are corrected for spatialvariations due to surface curvature using the above-described curvatureestimate. The resulting, corrected images represent the surfaceroughness slopes of substrate sample 24.

Prism Calibration

The intensity, I, associated with a location (x′,y′) on the sample andrecorded with the pixel at location (x,y) on CCD camera 18 is given by:I(x,y)=I _(min)(x,y)+I _(mod)(x,y)(1−cos(Ga(x′,y′)+b+c)/2

-   -   where:    -   I_(min) is the background intensity;    -   I_(mod) is the modulation intensity;    -   G is a calibration constant for a given prism;    -   a is the slope of the fine surface structure;    -   b is the phase associated with the prism position; and    -   c is the phase associated with the average slope of the sample.    -   (topographical extension of equation in Hartman et. al.,        Quantitative surface topography determination by Nomarski        reflection microscopy. 2: Microscope modification, calibration,        and planar sample experiments, Applied Optics, 1 Sep. 1980, Vol.        19, No 17)

Typically I_(min) is negligible or is removed using low pass filtering.An approximate linear response to surface slope is obtained with prism22 in a position such that (b+c)=π/2, and the above equation can beapproximated by:I(x,y)=I _(mod)(x,y)(1+Ga(x′,y′))/2.

In one method, an approximate linear response in the equation above isobtained by fixing a camera exposure time and adjusting the prism phaseposition b such that central tendency of the distribution of therecorded pixel values is approximately constant for each measuredsubstrate sample image. However, this technique confounds variations inthe light source intensity with prism phase position and does notadequately reduce measurement system variation for super-polishedsubstrates.

In another embodiment, the intensity modulation as (b+c) is varied from0 to π and is measured prior to substrate surface quality measurementsby adjusting b with prism 22 to achieve both an image intensity minimumand an image intensity maximum while illuminating a polished substratesample of superb quality and cleanliness. The distributions of pixelintensity values are used to determine and measure minimum intensity andmaximum intensity settings for prism 22. These minimum intensity andmaximum intensity measurements and images captured at the intensityminimum and maximum are utilized to set a position of prism 22 and inimage processing techniques which are described below. For calibrationof prism 22, a position of prism is set approximately to a locationwhich centers the distribution of pixel intensity values midway betweena minimum intensity and a maximum intensity, as described above. Whenprism 22 is positioned in this fashion, (b+c)=π/2 and the slope of thefine surface structure is linearly proportional to the intensity and asignal to noise ratio is increased for linear detection devices, forexample, CCD camera 18. The ratio of the pixel histogram centraltendency location to the exposure time at the estimated phase (b+c)=π/2determines the peak response ratio for the calibration method. Thistechnique for calibrating prism 22 is subject to error because themaximum intensity position is not always at (b+c)=π due to misalignmentof the prism as it is translated. Consequently, this technique does notsufficiently reduce measurement system variation for the highest qualitysuper-polished substrates.

In an alternative embodiment, the intensity modulation as (b+c) isvaried from 0 to π is measured prior to substrate surface qualitymeasurements by adjusting c with a mechanical stage to achieve both animage intensity minimum and an image intensity maximum whileilluminating a polished substrate sample of superb quality andcleanliness. Following the methods in the previous paragraph, themechanical stage is calibrated and used to set (b+c)=π/2 for substratemeasurements. In this method, the peak response ratio at phase (b+c)=π/2is found by adjusting the mechanical stage. The mechanical method is notsubject to prism misalignment error and provides the additionaladvantage of preserving the position of the optics throughout thecalibration and measurement process.

When substrate samples 24 are placed under a microscope, substratesamples 24 rarely have a background slope which is the same as areference image used in the prism calculation. The previously describedprism calibration includes adjusting a position of prism 22 for eachsubstrate sample 24 so that each image is recorded with the distributionof pixel intensity values approximately centered about the intensityassociated with (b+c)=π/2. Adjusting prism 22 for each sample ensures alinear intensity response for surface slope variations (i.e. sloperoughness) and increases a signal to noise ratio of the slopevariations. However, in high-resolution substrate testing, moving prism22 is undesirable since the movement of prism 22 creates errors in thefield of view compensation. In an alternative embodiment, a position ofprism 22 is fixed, and a stage is used to tilt the substrate under test,thereby varying c, until the distribution of intensity values isapproximately centered around the intensity associated with (b+c)=π/2.

In another embodiment, images of a clean low quality substrate arerecorded at several settings of the prism (or mechanical stage). Foreach picture, the camera exposure time is adjusted to achieve aspecified central tendency for the distribution of pixel values. Thefield of view of each image is normalized by dividing each pixel valueby the average intensity of local pixels. Then the standard deviation ofthe pixel values in each normalized image is calculated. Then, theexposure time is adjusted to the value where the standard deviation wasmaximized. Using this method, the peak response ratio is the ratio ofthe pixel histogram central tendency location to the exposure time whichmaximizes the standard deviation. For subsequent sample measurements,the ratio of the pixel central tendency value to the exposure shouldapproximately equal the peak response ratio. This is accomplished byeither adjusting the mechanical stage or the prism position. Differentcentral tendencies and exposure times may be used during samplemeasurements, provided that the ratio of the value of the centraltendency to exposure time is approximately equal to the ratio whichmaximized the standard deviation during calibration. The prism or stageadjustments performed in this way maximizes the image response tosurface slope variations and minimizes the measurement system variation.

Referring to FIG. 4, one possible embodiment of the above describedmethod of calibration is illustrated in flowchart 100. The methodillustrated by flowchart 100 is herein referred to as a coarse standardcalibration procedure. First, microscope 12 is setup 102 with a coarselypolished (low quality) substrate. Setup 102 refers to field of viewcompensation and focus compensation techniques, as described above, aswell as standard alignment procedures associated with differentialinterference microscopy. Prism 22 or mechanical stage is then adjusted104 to obtain a dark image of the substrate. An image is captured 106with a mode of the pixel histogram at about 75% of pixel range. Anintensity of each pixel is divided 108 by a local average pixelintensity. A standard deviation of image pixel intensity values iscalculated 110. The method is repeated at five to ten different settingsof prism 22 (shown in FIG. 1) or stage 28. A ratio of pixel histogramcentral tendency location to the exposure time which maximizes thesignal to noise of the surface structure data is described as a peakresponse ratio.

The standard deviations of pixel intensity are plotted 114, and anexposure time of camera 18 (shown in FIG. 1) is set 116 to a settingthat maximizes standard deviation. Substrates are then measured 118 byadjusting the prism or stage so that the mode of the histogram of pixelintensity values is at 75% of pixel range. The highest level for themode of the histogram should be used for calibration and measurements aslong as the CCD pixels are not saturated.

Operation

The above described methods are utilized to compensate for and calibratemicroscope 12 for use in determining a polish quality of a number ofsubstrate samples 24. To determine polish quality of each substratesample 24 (shown in FIG. 3) a user first places substrate sample 24under microscope 12. The user then focuses on substrate sample 24 usingeither of the above described aperture focus method or the eye/camerafocus offset method.

The user is able to adjust the intensity of the image being tested viaprism adjustment or stage tilt to achieve a specified mode of ahistogram of pixel values. The specified histogram value is determinedby the exposure time setting and the peak response ratio measured duringcalibration. The user then captures the image of substrate sample 24, orseveral images of the same position on substrate sample 24 if imageaveraging is to be used.

If the surface structure on substrate sample 24 is highly directional,in order to fully characterize the surface, additional images ofsubstrate sample 24 should be acquired after rotating the substratealong the optical axis of the microscope by 90 degrees.

After calibration of microscope 12 as described above with respect toFIG. 4, a method for determining surface quality of substrate sample 24is enabled, as described in detail above, and as illustrated in FIG. 5,which is a flowchart 150 for determining surface quality of substratesamples. Referring specifically to flowchart 150, focus of eyepiece 19and camera 18 utilizing the reference sample is calibrated 152 and phasebetween differential beams is also calibrated 154. Substrate sample 24is placed 156 under the microscope and illuminated 158 with light source14. The microscope focus focuses 160 on substrate sample 24, a phasebetween differential beams is adjusted 162, and at least one image ofsubstrate sample 24 is captured 164. Images of substrate sample 24 areprocessed 166, as further described below, to determine a level ofsurface structure on substrate sample 24.

Image Processing

In processing the captured images, if several images of the samelocation on substrate sample 24 were acquired, the images may beanalyzed separately, or as an average of the images. The resultingimage(s) to be analyzed is denoted as I.

Within an image I, each pixel value may be checked to determine if thevalue is outside of a preset limit. If so that pixel value is set to thelimit, so that false effects of particulates on the surface of thesubstrate are reduced, and further setting of the limit improves displaycontrast on computer 30. In one embodiment, the limits on pixel valuesare +/−three standard deviations from the average, and pixel valuesoutside of this limit are set to either + or − three standard deviationsfrom the average, depending on the original pixel value. Pixel valuesless than three standard deviations below the average are set to a valueequal to three standard deviations below the average. Pixel valuesgreater than three standard deviations above the average are set to avalue equal to three standard deviations above the average.

In one embodiment, captured images are compensated for variations inintensity modulation depth across the field of view. The substrateimages are compensated across the field of view by dividing thesubstrate image I by a reference image (REF) on a pixel by pixel basis.Field of view compensation creates an image with constant response tofine slope structure across the image and enhances fine structurecontrast in the displayed image. REF may be determined by severalmethods.

In one embodiment, REF is determined by using a reference standard asdescribed above. Several images of different locations on a superbquality substrate are recorded at the prism or stage setting where(b+c)=π/2. The average of these images (REF) represents the inputintensity variation across the field of view. Undesirable surfacestructure in REF is minimized by taking the average of images of severaldifferent locations on the superb quality substrate.

In an alternative embodiment, REF is generated by duplicating eachsubstrate measurement image and applying an averaging filter (to theduplicate) which replaces each pixel by the average of nearest neighborpixels with a certain pixel distance.

After pixel values are normalized, a two dimensional power spectraldensity is calculated, and displayed on computer 30. A user observesoff-axis correlations in the two dimensional image to determinesleek/scratch structure versus random roughness in the substrate sample.Additionally, a one dimensional power spectral density versus spatialfrequency is calculated and displayed on computer 30. The onedimensional power spectral density is integrated to determine the powerin certain spatial frequency bands. Some of the spatial frequency bandsin the power calculation are related to surface quality of a substrate,while others are related to camera noise and residual noise from inputintensity variation across the field of view. The exact spatialfrequencies depend on the application. In one embodiment, spatialfrequency bands in the range of 1 μm⁻¹ to 0.1 μm⁻¹ are used to assesssubstrate quality, with higher values in this spatial frequency rangeindicating lower quality substrates and lower values indicating higherquality substrates. As used herein, the term “sleeky” refers to asubstrate surface with a plurality of raised grooves that aresubstantially parallel to one another. As used herein the terms “sleek”and “sleek structure” refer to a plurality of raised grooves that aresubstantially parallel to one another as sometimes observed on asubstrate surface.

In another embodiment, a one-dimensional power spectral density iscalculated versus angle. The relative differences in the values of theoff-axis magnitudes of the power indicate a directionality ornon-directionality of the surface structure.

Correlation of x and y axes of the slope and surface images describe anamount of scratches and sleeks. In addition, Fast Fourier Transforms(FFTs) of the slope image and the topography image are used tocharacterize substrate sample roughness. FFTs with a high degree of xand y axis correlation (i.e. directional roughness) represent sleekysubstrate surfaces, while FFTs with low correlation between x and yindicate a uniformly rough surface. The two-dimensional FFTs areintegrated to give slope and surface power spectral densities as afunction of frequency. Furthermore, these spectral densities areintegrated over specified bandwidths of interest to simplifycharacterization of the substrate surfaces.

In another embodiment, an approximate three dimensional (3D) topographyis determined by integrating along a shear axis of prism 22. Thetopography aids in classifying substrate surface structure as being oneof dips, bumps, scratches, or contamination. Topography of sphericalparts appears to be parabolic after the image from microscope 12 isintegrated. The parabolic shape is then used to estimate curvature moreaccurately than the estimation from the slope image.

Algorithms are used to correctly integrate the image from microscope 12.Direct integration along the shear axis may be used, or an approximatemethod based on Fast Fourier Transform (FFT) techniques may be used.

The above described methods and systems therefore provide users withdata which represents a quality measurement of the polishing of asurface of substrates before those sample surfaces are coated with areflective material. Such processes are utilized to prevent substratesamples that do not have a properly polished surface from becomingcoated, and then being scrapped because light scattering properties ofthe mirrored surface are inadequate. In addition, substrate samples 24that do not have an adequately polished surface may be reworked, whichis inefficient and costly after the reflective material has beenapplied.

While the invention has been described in terms of various specificembodiments, those skilled in the art will recognize that the inventioncan be practiced with modification within the spirit and scope of theclaims.

1. A computer readable medium used to determine a surface quality ofsubstrate samples, said computer readable medium comprising codeconfigured to capture at least one image of a surface slope of asubstrate sample and process images of the surface slope to determine alevel of surface structure on the substrate sample to assess thesubstrate sample quality.
 2. A computer readable medium according toclaim 1 wherein said code is configured to: average samples for capturedimages of a substrate sample; calculate a power spectral density of theaveraged images; and determine power in frequency bands of the powerspectrum which are related to surface quality.
 3. A computer readablemedium according to claim 2 wherein to calculate a power spectraldensity said code is configured to: calculate two-dimensional powerspectral densities; and determine sleek structure versus randomroughness of the substrate sample using off-axis correlations.
 4. Acomputer readable medium according to claim 2 wherein to calculate apower spectral density said code is configured to: calculateone-dimensional power spectral densities; and analyze densities withinselected spatial frequency bands to assess substrate sample quality. 5.A computer readable medium according to claim 4 wherein to analyzedensities within selected spatial frequency bands to assess substratesample quality said code is configured to analyze densities within aselected spatial frequency band in a range of about 1 μm⁻¹ to about 0.1μm⁻¹.
 6. A method for determining a surface quality of substratesamples, said method comprising; capturing at least one image of asurface slope of a substrate sample; processing images of the surfaceslope; and determining a level of surface structure on the substratesample to assess the quality of the substrate sample and repair thesubstrate sample.
 7. A method according to claim 6 wherein processingimages of the surface slope comprises; averaging samples for thecaptured images of the substrate sample; calculating a power spectraldensity of the averaged samples; and determining power in frequencybands of a power spectrum, the frequency bands being related to surfacequality.
 8. A method according to claim 7 wherein calculating a powerspectral density comprises: calculating two-dimensional power spectraldensities; and determining sleek structure versus random roughness ofthe substrate sample using off-axis correlations.
 9. A method accordingto claim 7 wherein calculating a power spectral density comprises:calculating one-dimensional power spectral densities; and analyzingdensities within selected spatial frequency bands to assess substratesample quality.
 10. A method according to claim 9 wherein analyzingdensities within selected spatial frequency bands comprises analyzingdensities within a selected spatial frequency band in a range of about 1μm⁻¹ to about 0.1 μm⁻¹.
 11. A method according to claim 6 whereincapturing at least one image of a surface slope of a substrate samplecomprises: calibrating a microscope eyepiece focus with a focus of acamera that captures the images; and determining a peak response ratiofor the microscope through adjustment of phase between differentialbeams of the microscope.
 12. A method according to claim 11 whereincalibrating the microscope eyepiece focus with the camera focuscomprises placing an edge of a reference sample in the field of view ofthe camera.
 13. A method according to claim 6 wherein capturing at leastone image of a surface slope of a substrate sample comprises adjusting aphase between differential beams to attain the peak response ratio. 14.A method according to claim 13 wherein adjusting a phase betweendifferential beams comprises: adjusting to a plurality of positions atleast one of a prism and a slope of the reference sample; determiningwhich position provides a best structure contrast; and determining apeak response ratio which is the ratio of the central tendency of pixelvalues to The exposure time.
 15. A method according to claim 6 whereincapturing at least one image of a surface slope of a substrate samplecomprises capturing at least one image of the substrate sample in atleast two orientations.
 16. A method according to claim 6 furthercomprising adjusting a position of at least one of microscope prism anda slope of the substrate sample to a position such that a ratio of acentral tendency of pixel values to exposure time is approximately equalto the peak response ratio.